One of the most important themes of the novel is the way personal history and political history are constantly repeating themselves. Or if not exactly repeating, then at least "rhyming" with itself, as our old friend Mark Twain put it. One clever way García Márquez gets this across is to continuously recycle a handful of names for many, many characters down through many generations.
At one point, Úrsula suggests that all the men named José Arcadio are brawny, while all the Aurelianos are brainy, but this is kind of beside the point (and not even particularly true). More interesting is not just the repetition of the names but how fated and completely inescapable these names seem to be.
Several times in the novel, characters want to break the naming traditions but are entirely unable to or are prevented from doing so. Amaranta Úrsula wants to name her baby Rodrigo only to be outvoted by Aureliano (II) who names him Aureliano (III). Fernanda actually names her daughter Renata only to have everyone call her Meme, a diminutive of Remedios. And Meme refuses to name her child anything at all, only to have him called Aureliano (II) in honor of the family. All these characters are fated to share the same names and fated to lead horrible, doomed lives. Yikes, that's depressing.